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An Optimal Policy To Minimize Delay Costs Due To Waiting Time In A Queue

In: Recent Advances In Stochastic Operations Research

Author

Listed:
  • J. KOYANAGI

    (Tottori University, Koyama Minami 4-101, Tottori, 680-8552, Japan)

  • H. KAWAI

    (Tottori University, Koyama Minami 4-101, Tottori, 680-8552, Japan)

Abstract

We consider a discrete time queueing system. The service time and the interarrival time have geometric distributions. A decision maker(DM) arrives at the queue with two tasks, Task A and Task B. Task A must be processed by the server and DM must wait in the queue until it is finished if DM joins the queue. DM also needs a constant time to finish Task B. While DM is processing Task B, DM can interrupt Task B to join the queue and resume Task B after Task A is finished. There is a deadline for two tasks and the delay costs are incurred if two tasks are finished after the deadline. We consider a constant cost for breaking the deadline and a proportional cost for the delay from the deadline. We study the structure of the optimal policy to minimize the expected total delay costs.

Suggested Citation

  • J. Koyanagi & H. Kawai, 2007. "An Optimal Policy To Minimize Delay Costs Due To Waiting Time In A Queue," World Scientific Book Chapters, in: Tadashi Dohi & Shunji Osaki & Katsushige Sawaki (ed.), Recent Advances In Stochastic Operations Research, chapter 15, pages 225-234, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812706683_0015
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